Adhesion-stabilizing long-distance transport of cells on tissue surface

The stable transport of migrating eukaryotic cells is essential in organ development and repair processes. However, the mechanism that preserves transport stability over long distances in organs is not fully understood. As the driving mechanism of cell migration, the expressions of heterophilic cell-cell adhesion between moving cells and scaffolding tissue have been observed in such transport. In this paper, we theoretically investigate this heterophilic adhesion, which is persistently polarized in the migrating cell, as a possible transport stabilization mechanism. The adhesion was examined on the basis of the cellular Potts model, and our results confirm the stabilization of the transport to be an effect of the persistence.

Figure 1

(a) Schematic of cell transport on a tissue because of cell-cell adhesion. The arrows in cells represents the polarized direction of cell adhesion. The cross- and diagonal-hatched regions represent the high-density region of heterophilic adhesion molecules on the transported and scaffolding cells. (b) The unidirectional motion of transported cells. Arrows with dashed lines represent the migrating directions of cells.

Figure 2

(a) $|P_x|$ ($+$), $|P_y|$ ($\times$), and $\left|v_y-v_y^0\right|$ (*) as functions of ${\mathrm{\Gamma }}_{\mathrm{ha}}$. Snapshots of the simulation for (b) ${\mathrm{\Gamma }}_{\mathrm{ha}}=0.1$ and (c) ${\mathrm{\Gamma }}_{\mathrm{ha}}=0.5$. Yellow or orangelike (light) colored regions represent scaffolding cells and violet (dark) colored regions represent transported cells. Differences in color represent different cells. White regions represent empty space. Red arrows represent the polarities of cell adhesion. The directions of the coordination axes are given in (b).

Figure 3

(a) The mean-square distance of a cell motion $R^2$ for $N=1$ ($+$) and $N=8$ ($\times$) with ${\mathrm{\Gamma }}_{\mathrm{ha}}=0.5$ and $\tau =5.0$. The solid and dashed lines represent $t$ and $t^2$, respectively. (b) $|P_y|$ as a function of relaxation time of ${\mathit{p}}_m$, $\tau$ for ${\mathrm{\Gamma }}_{\mathrm{ha}}=0.1$ (solid line), ${\mathrm{\Gamma }}_{\mathrm{ha}}=0.2$ (dashed line), ${\mathrm{\Gamma }}_{\mathrm{ha}}=0.3$ (dotted line), ${\mathrm{\Gamma }}_{\mathrm{ha}}=0.4$ (dashed-dotted line). (c) The mean-square distance of a cell motion $R^2$ for $\tau =1$ ($+$), $\tau =3$ ($\times$), $\tau =5$ (*), $\tau =7$ ($⊡$), and $\tau =9$ ($\blacksquare$) with ${\mathrm{\Gamma }}_{\mathrm{ha}}=0.2$. The solid and dashed lines represent $t$ and $t^2$, respectively.

Figure 4

The schematic view of cell behavior and push due to heterophilic adhesion for (a) large ${\mathrm{\Gamma }}_{\mathrm{ha}}$ and for (b) small ${\mathrm{\Gamma }}_{\mathrm{ha}}$. (c) Magnified view of the leading edge. Solid and dashed arrows in (a) and (b) express the polarity and net motion, The solid arrow in (c) represents the push direction of the transported cell on the scaffold.